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API Error “Could not authenticate you” can be caused by next:

There were cases when client servers had some firewalling or other man-in-the-middle functionality that modified request headers. These headers normally contain authentication info which is checked by Twitter and if such request is modified then Twitter sends empty data. You should check for such behavior of your server then. Check any request filtering that can come from third-party plugins or server setup. We recommend to ask your hosting support team for this. Check PHP Parameter arg_separator.output in server’s php.ini. Default: &amp; while Twitter expects & symbol.

Twitter can blacklist specific IP or range of IPs of the whole hosting for abusing Twitter API. If you have shared hosting and someone on your hosting did abuse API then you can be affected by blacklist too. You should ask hosting to check this. Also, check Blacklisting section on Twitter Documentation